Wilmer went up the hill for $x$ minutes at a speed of $y$ kilometers per minute. Then he went down the same path at a speed of $z$ kilometers per minute, and it took him $w$ minutes to do it. Write an equation that relates $x$, $y$, $z$, and $w$.
Solution: Let's use the information we have to represent the distance Wilmer walked when he went up the hill and when he went down the hill. Since it is the same path, the two expressions are equal. For example, Wilmer went up the hill for $x$ minutes at a speed of $y$ kilometers per minute, so the total distance uphill is $x\cdot y$ kilometers: $\begin{aligned} &\phantom{=}\left(x\,\text{minutes}\right)\left(y\,\dfrac{\text{kilometers}}{\text{minute}}\right) \\\\ &=x\cdot y\,\cancel\text{minutes}\cdot\,\dfrac{\text{kilometers}}{\cancel\text{minute}} \\\\ &=x\cdot y\,\text{kilometers} \end{aligned}$ Similarly, the distance downhill was $z\cdot w$ kilometers. We know the two expressions should be equal, and so we get an equation: $x\cdot y=z\cdot w$